VPT2+K Spectroscopic Constants and Matrix Elements of the Transformed Vibrational Hamiltonian of a Polyatomic Molecule with Resonances Using Van Vleck Perturbation Theory

Authors

Andreana M. Rosnik, Hope College
William F. Polik, Hope CollegeFollow

Document Type

Article

Publication Date

7-16-2013

Publication Source

Molecular Physics

Volume Number

112

Issue Number

2

First Page

261

Last Page

300

Publisher

Taylor & Francis

ISSN

0026-8976

Comments

This is an Accepted Manuscript of an article published by Taylor & Francis in Molecular Physics on 16 Jul 2013, available online: http://www.tandfonline.com/10.1080/00268976.2013.808386

Abstract

Vibrational levels of polyatomic molecules are analysed with Van Vleck perturbation theory to connect experimental energy levels to computed molecular potential energy surfaces. Vibrational matrix elements are calculated from a quartic potential function via second-order Van Vleck perturbation theory, a procedure that treats both weak and strong interactions among vibrational states by approximately block-diagonalising the vibrational Hamiltonian. A clear and complete derivation of anharmonic and resonance constants as well as general expressions for both on- and off-diagonal matrix elements of the transformed Hamiltonian is presented. The equations are written in partial fraction form and as a constant multiplied by a harmonic oscillator matrix element to facilitate removing the effect of strongly interacting resonant states both in analytical formulae and in computer code. The derived equations are validated numerically, and results for the isotopomers of formaldehyde (H2CO, HDCO, D2CO) are included. The implications of the equations on zero-point energy calculations and experimental fits are discussed. The VPT2+K method is defined by these results for use in fitting and calculating vibrational energy levels.

Keywords

Molecular Vibrations, Van Vleck Perturbation Theory, Vibrational Energy Levels, Spectroscopic Constants, Resonances, Potential-energy Surfaces

Recommended Citation

Repository citation: Rosnik, Andreana M. and Polik, William F., "VPT2+K Spectroscopic Constants and Matrix Elements of the Transformed Vibrational Hamiltonian of a Polyatomic Molecule with Resonances Using Van Vleck Perturbation Theory" (2013). Faculty Publications. Paper 1066.
https://digitalcommons.hope.edu/faculty_publications/1066

Published in: Molecular Physics, Volume 112, Issue 2, July 16, 2013, pages 261-300. Copyright © 2013 Taylor & Francis, Milton Park, Abingdon.